Fairness in Learning: Classic and Contextual Bandits

Transcript

1. Fairness in Learning: Classic and Contextual Bandits Jamie Morgenstern joint w. Mathew Joseph, Michael Kearns, Aaron Roth University of Pennsylvania 1
2. Automated decisions of consequence 2 Hiring Lending Policing/ sentencing/ parole [Miller, 2015],[Byrnes, 2016] [Rudin, 2013], [Barry-Jester et al., 2015]
4. Each individual has inherent ‘quality’
5. Each individual has inherent ‘quality’ (expected revenue for giving a loan)
6. Each individual has inherent ‘quality’ (expected revenue for giving a loan)
7. Each individual has inherent ‘quality’ (expected revenue for giving a loan) entitling them to access to a resource
8. Each individual has inherent ‘quality’ (expected revenue for giving a loan) entitling them to access to a resource (high-revenue individuals deserve loans)
9. Each individual has inherent ‘quality’ (expected revenue for giving a loan) entitling them to access to a resource (high-revenue individuals deserve loans)
10. Each individual has inherent ‘quality’ (expected revenue for giving a loan) entitling them to access to a resource (high-revenue individuals deserve loans) Observe features, not qualities directly,
11. Each individual has inherent ‘quality’ (expected revenue for giving a loan) entitling them to access to a resource (high-revenue individuals deserve loans) Observe features, not qualities directly, must learn relationship
12. Each individual has inherent ‘quality’ (expected revenue for giving a loan) entitling them to access to a resource (high-revenue individuals deserve loans) Observe features, not qualities directly, must learn relationship (observe loan application)
13. Each individual has inherent ‘quality’ (expected revenue for giving a loan) entitling them to access to a resource (high-revenue individuals deserve loans) Observe features, not qualities directly, must learn relationship (observe loan application) (assume different for different groups!)
14. A source of bias in ML 4
15. A source of bias in ML 4 • Data feedback loops: only observe/update estimates for individuals current model believes are high- qualilty
16. A source of bias in ML 4 • Data feedback loops: only observe/update estimates for individuals current model believes are high- qualilty
17. We study 5
18. We study 5 A new notion of fairness: high-quality individuals must be treated as well as lower-quality individuals
19. We study 5 A new notion of fairness: high-quality individuals must be treated as well as lower-quality individuals And the “cost” of this constraint wrt learning rate R(T) (regret minimization)
20. We study 5 A new notion of fairness: high-quality individuals must be treated as well as lower-quality individuals And the “cost” of this constraint wrt learning rate R(T) (regret minimization) Fair learning rather than finding a fair model
21. Assumptions k groups each group has a function mapping features to ’qualities’ (initially unknown, belonging to C) (can be different for different groups)
22. Information/decision model Each day t [T] Observe feature vector from each group Choose one individual based on features Observe noisy estimate of quality of chosen Goal: maximize expected average quality
23. Fairness Definition 8
24. Fairness Definition 8 An algorithm A( ) is fair if, for all (0, 1]
25. Fairness Definition 8 with probability 1 An algorithm A( ) is fair if, for all (0, 1]
26. Fairness Definition 8 with probability 1 An algorithm A( ) is fair if, for all (0, 1] For any sequence x1, . . . , xT
27. Fairness Definition 8 for all rounds with probability 1 An algorithm A( ) is fair if, for all (0, 1] For any sequence x1, . . . , xT
28. Fairness Definition 8 for all rounds with probability 1 An algorithm A( ) is fair if, for all (0, 1] and all pairs of groups i, j For any sequence x1, . . . , xT
29. Fairness Definition 8 for all rounds with probability 1 An algorithm A( ) is fair if, for all (0, 1] and all pairs of groups i, j For any sequence x1, . . . , xT If E[quality of i at t] ≥ E[quality of j at t] then
30. Fairness Definition 8 for all rounds with probability 1 An algorithm A( ) is fair if, for all (0, 1] and all pairs of groups i, j For any sequence x1, . . . , xT If E[quality of i at t] ≥ E[quality of j at t] then A favors i over j in round t
31. Fairness Definition 8 for all rounds with probability 1 An algorithm A( ) is fair if, for all (0, 1] and all pairs of groups i, j For any sequence x1, . . . , xT If E[quality of i at t] ≥ E[quality of j at t] then P A chooses i at t | x1, . . . , xt P A chooses j at t | x1, . . . , xt
32. Separation between fair and unfair learning without features 9
33. Separation between fair and unfair learning without features 9 Theorem 1
34. Separation between fair and unfair learning without features 9 For any fair algo, R(T) = ˜ k3T . Theorem 1
35. Separation between fair and unfair learning without features 9 Without fairness one can achieve regret For any fair algo, R(T) = ˜ k3T . Theorem 1
36. Separation between fair and unfair learning without features 9 Without fairness one can achieve regret ˜ O( kT) For any fair algo, R(T) = ˜ k3T . Theorem 1
37. Feature-based fair learning 10 [Strehl and Littman, 2008] [ Li et al., 2011]
38. Feature-based fair learning 10 [Strehl and Littman, 2008] [ Li et al., 2011] Theorem 2 implications:
39. Feature-based fair learning 10 [Strehl and Littman, 2008] [ Li et al., 2011] Theorem 2 implications: There is a fair algorithm for d-dimensional linear mappings from features to qualities w. regret R(T) = O T1 c · poly(k, d, ln 1 )
40. Feature-based fair learning 10 [Strehl and Littman, 2008] [ Li et al., 2011] Theorem 2 implications: There is a fair algorithm for d-dimensional linear mappings from features to qualities w. regret R(T) = O T1 c · poly(k, d, ln 1 ) Any fair algorithm for d-dimensional conjunction mappings must have regret R(T) = Ω 2d
41. Fairness through Datamining - Pedreshi et al, ’08 - HDF ’13, HDFMB ’11, ZKC ’11, …. “Group” Fairness - CV ’10, FKL ’16, JL’15, KC ’11, KKZ ’12, KAAS ’12… “Individual” Fairness - Dwork et al, 2012 - Johnson, Foster, Stine ’16 - Hardt, Price, Srebro ’16 - Kleinberg, Mullainathan, Raghavan ’16 11 Related Work
42. Fairness through Datamining - Pedreshi et al, ’08 - HDF ’13, HDFMB ’11, ZKC ’11, …. “Group” Fairness - CV ’10, FKL ’16, JL’15, KC ’11, KKZ ’12, KAAS ’12… “Individual” Fairness - Dwork et al, 2012 - Johnson, Foster, Stine ’16 - Hardt, Price, Srebro ’16 - Kleinberg, Mullainathan, Raghavan ’16 11 Related Work Our work focuses on fair learning rather than finding a fair model
43. Conclusions 12
44. Conclusions 12 New notion of fairness: higher-quality ⇒ better treatment
45. Conclusions 12 Must be *confident* about relative qualities before preferential treatment ensues New notion of fairness: higher-quality ⇒ better treatment
46. Conclusions 12 There’s a cost to fairness Must be *confident* about relative qualities before preferential treatment ensues New notion of fairness: higher-quality ⇒ better treatment
47. Conclusions 12 There’s a cost to fairness in some cases, this cost is mild, in others, great Must be *confident* about relative qualities before preferential treatment ensues New notion of fairness: higher-quality ⇒ better treatment
48. Conclusions 12 There’s a cost to fairness in some cases, this cost is mild, in others, great Must be *confident* about relative qualities before preferential treatment ensues New notion of fairness: higher-quality ⇒ better treatment Thanks!